Buckling of a functionally graded coating with an embedded crack bonded to a homogeneous substrate

Sami El-Borgi, W. Aloulou, A. Zghal

Research output: Contribution to journalArticle

13 Citations (Scopus)


In an attempt to simulate buckling of nonuniform coatings, we consider the problem of an embedded crack in a functionally graded coating bonded to a homogeneous substrate subjected to a compressive loading. The coating is graded in the thickness direction and the material gradient is orthogonal to the crack direction which is parallel with the free surface. The loading consists of a uniform compressive strain applied away from the crack region. The graded coating is modeled as a nonhomogeneous medium with an isotropic stress-strain law. Using a nonlinear continuum theory and a suitable perturbation technique, the plane strain problem is reduced to an eigenvalue problem describing the onset of buckling. Using integral transforms, the resulting plane elasticity equations are converted analytically into singular integral equations which are solved numerically to give the critical buckling strain and the corresponding crack opening displacement shapes. The main objective of the paper is to study the influence of material nonhomogeneity on the buckling resistance of the graded layer for various crack positions and coating thicknesses.

Original languageEnglish
Pages (from-to)137-150
Number of pages14
JournalInternational Journal of Fracture
Issue number1-2
Publication statusPublished - Nov 2006
Externally publishedYes



  • Buckling
  • Functionally graded coating
  • Instability load
  • Nonlinear continuum theory
  • Perturbation technique
  • Singular integral equations

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials

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